complex evaluation (1 Viewer)

Lith_30

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using the diagram from part i or just by solving for the roots of unity and and

now the expression can be simplified to cause

then we just sub in and in

 

chilli 412

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what else could equal to?
Screen Shot 2022-11-21 at 12.55.16 pm.png
i was playing around with this on desmos and found out z1 can actually be an infinite number of complex numbers with argument less than pi/2 , all the complex numbers have a modulus of 1 as well, here is the desmos link (i spent a long time doing this in business studies) desmos link
 

Drongoski

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what else could equal to?


You can argue geometrically that the sum of the squares of the distances remains unchanged (is invariant) when we rotate the figure anticlockwise until theta = 0 (your special case) or any other angle.
 
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Drongoski

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View attachment 37090
i was playing around with this on desmos and found out z1 can actually be an infinite number of complex numbers with argument less than pi/2 , all the complex numbers have a modulus of 1 as well, here is the desmos link (i spent a long time doing this in business studies) desmos link
Nice diagram. But the 3 red lines must be equal in length, being radii of the unit circle.
 

Lith_30

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View attachment 37090
i was playing around with this on desmos and found out z1 can actually be an infinite number of complex numbers with argument less than pi/2 , all the complex numbers have a modulus of 1 as well, here is the desmos link (i spent a long time doing this in business studies) desmos link
interesting graph, have a look at this graph which probably shows the question better and also helps demonstrate what @Drongoski was saying about the anser being independent of the argument of z1.
 

chilli 412

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interesting graph, have a look at this graph which probably shows the question better and also helps demonstrate what @Drongoski was saying about the anser being independent of the argument of z1.
oh woops i just tested my one with a circle of radius 1 and they arent all one ill try to fix it
 

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